{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 离散傅里叶变换"
   ]
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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "   离散傅里叶变换（即 DFT）是数字信号处理的首要工具。该产品的基础是快速傅里叶变换 (FFT)，这是一种可减少执行时间的 DFT 计算方法。许多工具箱函数（包括 Z 域频率响应、频谱和倒频谱分析，以及一些滤波器设计和实现函数）都支持 FFT。\n",
    "   MATLAB® 环境提供 fft 和 ifft 函数，分别用于计算离散傅里叶变换及其逆变换。对于输入序列 x 及其变换版本 X（围绕单位圆的等间隔频率的离散时间傅里叶变换），这两个函数实现以下关系\n",
    "![image.png](attachment:image.png)\n",
    "   和\n",
    "![image.png](attachment:image.png)\n",
    "在这些方程中，序列下标从 1 而不是 0 开始，因为采用 MATLAB 向量索引方案，并且\n",
    "![image.png](attachment:image.png)\n",
    "注意  MATLAB 约定是对 fft 函数使用负 j。这是工程约定；物理和纯数学通常使用正 j。\n",
    "使用单个输入参数 x 的 fft 计算输入向量或矩阵的 DFT。如果 x 是向量，fft 计算向量的 DFT；如果 x 是矩形数组，fft 计算每个数组列的 DFT。\n",
    "例如，创建时间向量和信号："
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要以度为单位绘制幅值和相位，请键入以下命令："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "import numpy as np\n",
    "from scipy.fftpack import fft\n",
    "\n",
    "t=np.arange(0,10,1/100)\n",
    "x=np.array([np.sin(2*pi*15*t) +np.sin(2*pi*40*t)])\n",
    "y=fft(x)\n",
    "y=y.reshape(len(t))\n",
    "m=abs(y)\n",
    "y[m<1e-6]=0\n",
    "p=np.unwrap(np.angle(y))\n",
    "\n",
    "f=np.arange(0,len(t),1)*100/len(t)\n",
    "plt.subplot(211)\n",
    "plt.plot(f,m)\n",
    "plt.title('Magnitude')\n",
    "plt.xticks([15,40,60,85])\n",
    "plt.subplot(212)\n",
    "plt.plot(f,p*180/pi)\n",
    "plt.title('Phase')\n",
    "plt.xticks([15,40,60,85])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "fft的第二个参数指定变换的点数 n，表示 DFT 的长度：\n",
    "Matlab实现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "import numpy as np\n",
    "from scipy.fftpack import fft\n",
    "\n",
    "t=np.arange(0,10,1/100)\n",
    "x=np.array([np.sin(2*pi*15*t) +np.sin(2*pi*40*t)])\n",
    "n=512\n",
    "y=fft(x,n)\n",
    "y=y.reshape(n)\n",
    "m=abs(y)\n",
    "p=np.unwrap(np.angle(y))\n",
    "f=np.arange(0,n,1)*100/n\n",
    "\n",
    "plt.subplot(211)\n",
    "plt.plot(f,m)\n",
    "plt.title('Magnitude')\n",
    "plt.xticks([15,40,60,85])\n",
    "\n",
    "plt.subplot(212)\n",
    "plt.plot(f,p*180/pi)\n",
    "plt.title('Phase')\n",
    "plt.xticks([15,40,60,85])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在本例中，如果输入序列比 n 短，fft 会用零填充输入序列，如果输入序列比 n 长，则会截断序列。如果未指定 n，则默认为输入序列的长度。fft 的执行时间取决于其执行的 DFT 的长度 n；有关该算法的详细信息，请参阅 fft 参考页。\n",
    "注意：得到的 FFT 幅值是 A*n/2，其中 A 是原始幅值，n 是 FFT 点数。仅当 FFT 点的数量大于或等于数据样本的数量时，上述情形才成立。如果 FFT 点数小于数据样本数，则 FFT 幅值比原始幅值低上述量。\n",
    "离散傅里叶逆变换函数 ifft 也接受输入序列以及可选的变换所需点数。尝试以下示例；原始序列 x 和重新构造的序列是相同的（在舍入误差内）。\n",
    "Matlab 实现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from math import pi\n",
    "import numpy as np\n",
    "from scipy.fftpack import fft, ifft\n",
    "t=np.arange(0,1,1/255)\n",
    "x=np.array([np.sin(2*pi*120*t)])\n",
    "y=np.real(ifft(fft(x)))\n",
    "x=x.reshape(len(t))\n",
    "y=y.reshape(len(t))\n",
    "plt.plot(t,x-y)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
